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E. G. D. Cohen

Publications and source records attributed to E. G. D. Cohen.

At least 19 recordsLinked to original sources
arXiv2017

Nonequilibrium Langevin dynamics: a demonstration study of shear flow fluctuations in a simple fluid

The present study is based on a recent success of the second-order stochastic fluctuation theory in describing time autocorrelations of equilibrium and nonequilibrium physical systems. In particular, it was shown to yield values of the related deterministic parameters of the Langevin equation for a Couette flow in a microscopic Molecular Dynamics model of a simple fluid. In this paper we find all the remaining constants of the stochastic dynamics, which is then numerically simulated and directly compared with the original physical system. By using these data, we study in detail the accuracy and precision of a second-order Langevin model for nonequilibrium physical systems, theoretically and computationally. In addition, an intriguing relation is found between an applied external force and cumulants of the resulting flow fluctuations. This is characterized by a linear dependence of athermal cumulant ratio, a new quantity introduced here.

cond-mat.stat-mech↗
arXiv2016

Second-order fluctuation theory and time autocorrelation function for currents

By using recent developments for the Langevin dynamics of spatially asymmetric systems, we routinely generalize the Onsager-Machlup fluctuation theory of the second order in time. In this form, it becomes applicable to fluctuating variables, including hydrodynamic currents, in equilibrium as well as nonequilibrium steady states. From the solution of the obtained stochastic equations we derive an analytical expression for the time autocorrelation function of a general fluctuating quantity. This theoretical result is then tested in a study of a shear flow by molecular dynamics simulations. The proposed form of the time autocorrelation function yields an excellent fit to our computational data for both equilibrium and nonequilibrium steady states. Unlike the analogous result of the first-order Onsager-Machlup theory, our expression correctly describes the short-time correlations. Its utility is demonstrated in an application of the Green-Kubo formula for the transport coefficient. Curiously, the normalized time autocorrelation function for the shear flow, which only depends on the deterministic part of the fluctuation dynamics, appears independent of the external shear force in the linear nonequilibrium regime.

cond-mat.stat-mech↗
arXiv2016

The Langevin equation for systems with a preferred spatial direction

In this paper, we generalize the theory of Brownian motion and the Onsager-Machlup theory of fluctuations for spatially symmetric systems to equilibrium and nonequilibrium steady-state systems with a preferred spatial direction, due to an external force. To do this, we extend the Langevin equation to include a bias, which is introduced by the external force and alters the Gaussian structure of the system's fluctuations. By solving this extended equation, we demonstrate that the statistical properties of the fluctuations in these systems can be predicted from physical observables, such as the temperature and the hydrodynamic gradients.

cond-mat.stat-mech↗
arXiv2016

Subdiffusion, Anomalous Diffusion and Propagation of a Particle Moving in Random and Periodic Media

We investigate the motion of a single particle moving on a two-dimensional square lattice whose sites are occupied by right and left rotators. These left and right rotators deterministically rotate the particle's velocity to the right or left, respectively and \emph{flip} orientation from right to left or from left to right after scattering the particle. We study three types of configurations of left and right rotators, which we think of as types of media, through with the particle moves. These are completely random (CR), random periodic (RP), and completely periodic (CP) configurations. For CR configurations the particle's dynamics depends on the ratio $r$ of right to left scatterers in the following way. For small $r\simeq0$, when the configuration is nearly homogeneous, the particle subdiffuses with an exponent of 2/3, similar to the diffusion of a macromolecule in a crowded environment. Also, the particle's trajectory has a fractal dimension of $d_f\simeq4/3$, comparable to that of a self-avoiding walk. As the ratio increases to $r\simeq 1$, the particle's dynamics transitions from subdiffusion to anomalous diffusion with a fractal dimension of $d_f\simeq 7/4$, similar to that of a percolating cluster in 2-d. In RP configurations, which are more structured than CR configurations but also randomly generated, we find that the particle has the same statistic as in the CR case. In contrast, CP configurations, which are highly structured, typically will cause the particle to go through a transient stage of subdiffusion, which then abruptly changes to propagation. Interestingly, the subdiffusive stage has an exponent of approximately 2/3 and a fractal dimension of $d_f\simeq4/3$, similar to the case of CR and RP configurations for small $r$.

cond-mat.stat-mech↗
arXiv2015

Asymmetry of steady state current fluctuations in nonequilibrium systems

For systems in nonequilibrium steady states, a novel modulated Gaussian probability distribution is derived to incorporate a new phenomenon of biased current fluctuations, discovered by recent laboratory experiments and confirmed by molecular dynamics simulations. Our results consistently extend Onsager-Machlup fluctuation theory for systems in thermal equilibrium. Connections with the principles of Statistical Mechanics due to Boltzmann and Gibbs are discussed. At last, the modulated Gaussian distribution is of potential interest for other statistical disciplines, which make use of the Large Deviation theory.

cond-mat.stat-mech↗
arXiv2015

Self-Limiting Trajectories of a Particle Moving Deterministically in a Random Medium

We study the motion of a particle moving on a two-dimensional honeycomb lattice, whose sites are randomly occupied by either right or left rotators, which rotate the particle's velocity to its right or left, according to deterministic rules. In the model we consider, the scatterers are each initially oriented to the right with probability $p\in[0,1]$. This is done independently, so that the initial configuration of scatterers, which forms the medium through which the particle moves, are both independent and identically distributed. For $p\in(0,1)$, we show that as the particle moves through the lattice, it creates a number of reflecting structures. These structures ultimately \emph{limit} the particle's motion, causing it to have a periodic trajectory. As $p$ approaches either 0 or 1, and the medium becomes increasingly homogenous, the particle's dynamics undergoes a discontinuous transition from this self-limiting, periodic motion to a self-avoiding motion, where the particle's trajectory, away from its initial position, is a self-avoiding walk. Additionally, we show that the periodic dynamics observed for $p\in(0,1)$ can persist, even if the initial configuration of scatterers are not identically distributed. Furthermore, we show that if these orientations are not chosen independently, this can drastically change the particle's motion causing it to have a behavior that is nonperiodic.

math-ph↗
arXiv2015

On the Transition of a Non-Equilibrium System to an Equilibrium System

It is shown that the most important feature of Non-Equilibrium Thermodynamics is not the entropy production, but the organization of the currents in order to flow. This is also needed to obtain the maximum entropy in the equilibrium state, as is required by Equilibrium Thermodynamics.

cond-mat.stat-mech↗
arXiv2014

Self-Avoiding Modes of Motion in a Deterministic Lorentz Lattice Gas

We study the motion of a particle on the two-dimensional honeycomb lattice, whose sites are occupied by either flipping rotators or flipping mirrors, which scatter the particle according to a deterministic rule. For both types of scatterers we find a new type of motion that has not been observed in a Lorentz Lattice gas, where the particle's trajectory is a self-avoiding walk between returns to its initial position. We show that this behavior is a consequence of the deterministic scattering rule and the particular class of initial scatterer configurations we consider. Since self-avoiding walks are one of the main tools used to model the growth of crystals and polymers, the particle's motion in this class of systems is potentially important for the study of these processes.

math-ph↗
arXiv2014

Clausius' Entropy Revisited

Conventional Non-equilibrium Thermodynamics is mainly concerned with systems in local equilibrium and their entropy production, due to the irreversible processes which take place in these systems. In this paper fluids will be considered in a state of local equilibrium. We argue that the main feature of such systems is not the entropy production, but the organization of the flowing currents in such systems. These currents do not only have entropy production, but must also have an organization needed to flow in a certain direction. It is the latter, which is the source of the equilibrium entropy, when the fluid goes from a local equilibrium state and to an equilibrium state. This implies a transmutation of the local equilibrium current's organization into the equilibrium entropy. Alternatively, when a fluid goes from an equilibrium state to a local equilibrium state, its entropy transmutes into the organization of the currents of that state.

cond-mat.stat-mech↗
arXiv2013

Note on the nature of the transition between a system in an equilibrium state and a system in a non-equilibrium state (and vice-versa)

The transition from a non-equilibrium state to an equilibrium state is characterized not only by the disappearance of the entropy production, but mainly by the disappearance of the organized currents, due to the gradients present in a non-equilibrium system. Their disappearance is necessary to obtain maximum entropy in the equilibrium state.

cond-mat.stat-mech↗
arXiv2013

Einstein and Boltzmann: Determinism and Probability or The Virial Expansion Revisited

Boltzmann's Principle S = k ln W was repeatedly criticized by Einstein since it lacked a proper dynamical foundation in view of the thermal motion of the particles, out of which a physical system consists. This suggests, in particular, that the statistical mechanics of a system in thermal equilibrium should be based on dynamics. As an example, a dynamical derivation of the density expansions of the two-particle distribution function, as well as of the thermodynamic properties of a moderately dense gas in thermal equilibrium, is outlined here. This is a different derivation than the usual one based on Gibbs' probabilistic canonical ensemble, where dynamics is eliminated at the beginning and equilibrium statistical mechanics is reduced to statics. It is argued that the present derivation in this paper could, in principle, also be applied to other equilibrium properties and perhaps also to other fields.

cond-mat.stat-mech↗
arXiv2011

Green-Kubo relation for viscosity tested using experimental data for a 2D dusty plasma

The theoretical Green-Kubo relation for viscosity is tested using experimentally obtained data. In a dusty plasma experiment, micron-size dust particles are introduced into a partially-ionized argon plasma, where they become negatively charged. They are electrically levitated to form a single-layer Wigner crystal, which is subsequently melted using laser heating. In the liquid phase, these dust particles experience interparticle electric repulsion, laser heating, and friction from the ambient neutral argon gas, and they can be considered to be in a nonequilibrium steady state. Direct measurements of the positions and velocities of individual dust particles are then used to obtain a time series for an off-diagonal element of the stress tensor and its time autocorrelation function. This calculation also requires the interparticle potential, which was not measured experimentally, but was obtained using a Debye-Hückel-type model with experimentally determined parameters. Integrating the autocorrelation function over time yields the viscosity for shearing motion amongst dust particles. The viscosity so obtained is found to agree with results from a previous experiment using a hydrodynamical Navier-Stokes equation. This comparison serves as a test of the Green-Kubo relation for viscosity. Our result is also compared to the predictions of several simulations.

physics.plasm-ph↗
arXiv2010

Stick-slip motion of solids with dry friction subject to random vibrations and an external field

We investigate a model for the dynamics of a solid object, which moves over a randomly vibrating solid surface and is subject to a constant external force. The dry friction between the two solids is modeled phenomenologically as being proportional to the sign of the object's velocity relative to the surface, and therefore shows a discontinuity at zero velocity. Using a path integral approach, we derive analytical expressions for the transition probability of the object's velocity and the stationary distribution of the work done on the object due to the external force. From the latter distribution, we also derive a fluctuation relation for the mechanical work fluctuations, which incorporates the effect of the dry friction.

cond-mat.stat-mech↗
arXiv2009

Path integral approach to random motion with nonlinear friction

Using a path integral approach, we derive an analytical solution of a nonlinear and singular Langevin equation, which has been introduced previously by P.-G. de Gennes as a simple phenomenological model for the stick-slip motion of a solid object on a vibrating horizontal surface. We show that the optimal (or most probable) paths of this model can be divided into two classes of paths, which correspond physically to a sliding or slip motion, where the object moves with a non-zero velocity over the underlying surface, and a stick-slip motion, where the object is stuck to the surface for a finite time. These two kinds of basic motions underlie the behavior of many more complicated systems with solid/solid friction and appear naturally in de Gennes' model in the path integral framework.

cond-mat.stat-mech↗
arXiv2009

Anomalous fluctuation relations

We complement and extend our work on fluctuation relations arising in nonequilibrium systems in steady states driven by Lévy noise [Phys. Rev. E 76, 020101(R) (2006)]. As a concrete example, we consider a particle subjected to a drag force and a Lévy white noise with tail index $μ\in (0,2]$, and calculate the probability distribution of the work done on the particle by the drag force, as well as the probability distribution of the work dissipated by the dragged particle in a nonequilibrium steady state. For $0<μ<2$, both distributions satisfy what we call an anomalous fluctuation relation, characterized by positive and negative fluctuations that asymptotically have the same probability. For $μ=2$, by contrast, the work and dissipated work distributions satisfy the known conventional and extended fluctuation relations, respectively, which are both characterized by positive fluctuations that are exponentially more probable than negative fluctuations. The difference between these different fluctuation relations is discussed in the context of large deviation theory. Experiments that could probe or reveal anomalous fluctuation relations are also discussed.

cond-mat.stat-mech↗
arXiv2009

Steady state work fluctuations of a dragged particle under external and thermal noise

We consider a particle, confined to a moving harmonic potential, under the influence of friction and external asymmetric Poissonian shot noise (PSN). We study the fluctuations of the work done to maintain this system in a nonequilibrium steady state. PSN generalizes the usual Gaussian noise and can be considered to be a paradigm of external noise, where fluctuation and dissipation originate from physically independent mechanisms. We consider two scenarios: (i) the noise is given purely by PSN and (ii) in addition to PSN the particle is subject to white Gaussian noise. In both cases we derive exact expressions for the large deviation form of the work distribution, which are characterized by the time scales of the system. We show that the usual steady state fluctuation theorem is violated in our model and that in a certain parameter regime large negative work fluctuations are more likely to occur than the corresponding positive ones, though the average work is always positive.

cond-mat.stat-mech↗